Square Uv map: fill the Uv layout
Hopefully your 2D cursor is at the bottom left of your UV layout image area - if not, position it there.

In toolbar area, choose "2D Cursor" as Rotation/Scaling Pivot.

In the UVs menu --> select "Constrain to Image Bounds"

Now select all of the vertices in your UV.

If the island is not flush with the bottom left: grab (G) and move so the edges are flush with the bottom left (the constraint will ensure that you cannot drag the island past the bounds)

Now, scale (S) - you should be able to scale to the image bounds.